Is this a bug?
hypergeom([1, -1, 1/2], [-12,-3], 1);
Error, (in hypergeom/check_parameters) function doesn't exist: missing appropriate negative integers in the first list of parameters to compensate the negatives integer(s): [-3], found in the second list.
Yet this hypergeometric series terminates and Maple should be able to handle it, at least according to the Maple help page (the second rule below applies, yet the numerator has a smaller absolute value, so the first rule below applies).
If some n[i] is a non-positive integer, the series is finite (that is, F(n, d, z) is a polynomial in z).
If some d[j] is a non-positive integer, the function is undefined for all non-zero z, unless there is also a negative upper parameter of smaller absolute value, in which case the previous rule applies.
Interestingly, the Wolfram Mathematica app can evaluate this to 311/312.